Will unlocking a 4G phone make it 3G when switching carriers?

So when I switched from ATT to Tmo my blackberry I was told was now running on 2g rather than the original 3g. The phone died shortly after I switched so I didn't really get a chance to check the speed. Anyway, it was somthing tmo told me, is it true or is it something they say to get you to buy their phones? If it's true, is it the carrier switching or unlocking process that causes this generational change? I ask because I see a 4g phone on ebay I may want to buy that says it's unlocked for any carrier, I don't know who the original carrier was or if it matters. Thanks!

 

Okay thanks. I am still not completely clear though? Can the act of unlocking solely change the the speed from 4G to 3G? Meaning if it's a TMO phone, the other person unlocks it, you then use it on TMO, would it go down a generation? Versus switching from TMO to ATT or ATT to TMO as well as unlocking.

 

OK that helps a lot. I moved from ATT to TMO. But that TMO BB phone died so now I am in need of a new phone. I guess that means I need to look for a TMO one because if I find a ATT one then I risk speed issue decreases. No need to pay for 4G phone but get 3G.