I need to play more good Yoshis, but at this point I would say this match-up is either 50/50 or maybe even 55/45 in favor of Mega Man.
The reason is that we have some very effective ways of edgeguarding against Yoshi once he's off stage.
I know I'm carving myself out a niche as the "Leaf Shield" guy on these forums, but LS really kills Yoshi's ability to go for a ledge grab. If you think he's going to recover to ledge, all you have to do is fire up LS, run off the stage, and snap to ledge grab.
Your invincibility frames will protect you from anything Yoshi can throw at you, and the leaves will hitstun him out of his double jump and attacks, preventing him from grabbing the stage. (His super armor protects him against knockback, not hitstun.) From there it's just a simple matter of following up with a bair or footstool to seal the stock.
Also, unlike other characters, Yoshi doesn't get his full UpB recovery back after a footstool-- IIRC, he has to land on stage to get his "egg bounces" back. So he's quite susceptible to footstool gimps.
I've done this against a lot of scrubbier Yoshis and it just plain works. After a while they learn that they HAVE to recover high against you if they don't want to get gimped, which makes them predictable and easier to smack around with bairs and uairs. Sometimes I'll just activate a LS and jump up and down to spook them -- if they recover high, I full hop air dodge at them to get a few hits and kill their momentum, giving myself a chance at a follow up, and if they recover low I do the ledge gimp.
The inverse is not true for Yoshi -- our ability to fast fall at high speeds, cover our recoveries with projectiles, instantly gain height from Rush, and attack after our UpB makes us a lot more unpredictable and difficult to edge guard.
There's a lot more to this match up, of course, and Yoshi has a really nasty rushdown game to deal with on the stage. But our offstage and ledge guarding game is plainly superior to his, IMO.