I'm playing on a Yamaha bass trombone 59L-GP mouthpiece on a tenor trombone and i can control my sound fine, even play with a big sound. but my private lesson teacher is telling me to switch to a smaller mouthpiece since i play lead in my bands, both jazz and concert.

I have a 6 1/2 Al and a 5G but they're not working for me, for some reason its hard to control my sound and I've worked and worked on it but nothing changes. Could it have something to do with the balances of the mouthpieces? The cup rim size? I'm not sure but I'd rather not switch but if i have to i want to switch to something that's going to help me not hurt me.

Oh yea, and i can still reach the high register with the 59L-GP, my private lesson teacher says i need something smaller so i will stick out above the other trombones in the section.

Any suggestions or comments would be greatly appreciated

I actually used to do the exact same thing. I played principle in college wind ensemble and orchestra on a Marcinkowicz Georde Roberts custom, and got a great sound out of it, even in the higher register. I eventually tried other pieces, both for more consistency in all registers and more endurance in the upper, as well as a better sound to cut through. After trying many peices I finally settles on a Warburton 7ST, and am now again looking for something a bit more open. I would love to try some Greg Black Alessi pieces, but I need to find a store that has them to try out before I buy.

Anyway, back to the point. I had the same issue you hace, the 6 1/2 and 5 where both just too small, and I did not like the thin sound I got out of them. You should go out and try as many different brands and sizes you can till you find something that gives you exactly what you need and also matches the horn better.

I sense a common problem here....(and this is just a hunch, so if I'm wrong please forgive me!)
It sounds to me like you, at some point along the way, fell in love with the large horn classical sound. That's great. But... in a big band, that sound just isn't going to fly. You need to find that balance... a sound that projects, has a bit of an edge to it, but still as a sweet tone. You're looking to blend with the trumpet section, and if you're the lead, blend with the lead trumpet. It's a hard thing to do, especially when you're trying to match those tight articulations on a big tubby horn and mouthpiece.
It sounds like you are trying to play with your big-horn-pretty-legit sound in the big band, and your teacher senses that it doesn't blend, nor does it give the desired sound. It doesn't matter that you can hit the notes. It's a sound he's after. His suggestion is to go smaller on the mouthpiece, which may or may not work. But until you embrace the big band/lead bone sound, no horn/mouthpiece combination is going to work.
You have to treat lead/bigband bone playing almost like an entirely different instrument. They're supposed to sound different. You should approach them that way.
Now... when you get that sound concept in your head, it is possible to get it with a large rimmed mouthpiece, if you have a shallow cup and tighter backbore. The bad news is, the only way I know of to get a mouthpiece like that is through Doug Elliott... his stuff is great, but you'll wait and it ain't cheap.
But it just sounds to me like another case of getting the right tool for the job.
I played in a showband all last year with a second bone player who insisted on playing on a Bach 42 (while I was playing lead on a 3B). It just didn't blend. It drove me nuts.
Again, just something to think about. If i'm way off base here, just ignore me.

One more thing...
If switching back and forth makes you nervous (and I can completely understand why it would)...
I used to switch back and forth between two very different sized mouthpieces and it was a real problem for me. Now, I use a rim size equivalent to somewhere between a Bach 3 and 4 on both my lead horn and my concert horn. But the large horn mpc has a deep cup and open backbore, while the lead mpc is a very shallow cup and tight backbore.
The sounds are very different, but they feel exactly the same on my face. It makes switching very easy. It has made a huge difference for me. (Thank you Doug Elliott!!!!)

The problem on the 6 1/2 Al and the 5G is that i can't control the sound in the middle B Flat Partial (mostly F sharp) my high register has a good sound. I play on a Benge 165F and a lot of air has to be put through it to get a good sound and the 6 1/2 Al and the 5G aren't as open as my 59L-GP is. But on the other hand it might not be the Benge 165F because i also have a king 606 and i find the same problem.

How long have you been playing?
My music teacher and most music teachers start their students off on a 12c mouthpiece which is small. Most student horns come with this mouthpiece. Its like the 7c mouthpiece for trunmpet, it restricts you a little on flexibility, but it helps you learn to control your sound and helps you hit the right partial. Believe me, when I switched from the 12c to a 5g mouthpiece, the 5g was huge, but I was able to play it because of the the way the 12c trained me. I find the 6 1/2 AL better than the 5g, but the 5g puts less restraint on your lips. Also, I switch to the 12c a little in jazz because it allows me to hit a Bb5 relatively easy.

Also, for bass trombone I play on a 1 1/2 g by holton.

i've been playing for 4 years, i'm a sophomore.
and i can hit the right partials but i cant control the sound in the middle B flat partial, like i get that double lip buzz sound. this only happens on a 5G and a 6 1/2 Al

Be patient. Mouthpiece changes are a big thing. Pick one of those mouthpieces, or get a new one you like, and work hard on your fundamentals. For those notes that don't sound right, work on your mouthpiece alone trying to find that exact note. It is a big change going from a bass piece to a tenor piece for the same music. Just be patient, do your fundamental work, mouthpiece buzzing and it will work out. Especialy with your teacher helping. Trust me, the change will be worth it. It was for me.

By the way, if it's a specific jazz band/lead bone issue, I agree completely with Steve. It's all about the sound output you are after. Try to find a modular system for your piece, and use the same rim, but diferent backbores for different groups, jazz vs classical. Greg Black makes amazing pieces, but the one I use is made by Warburton. (Of course, that's only because I have not had the oportunity to test GB pieces, and I refuse to buy before I try.) Same idea, different dude, and I love it for most playing.