It usually kills in that diagonal area you describe, but I'm basing this mostly off of neutrals stages, not the counter picks. I see it kill vertically a lot on stages with lower ceilings.
My general opinion with sparce explanation (Order is irrelevant):
Good
Pictochat
Yoshi's Island (Pipes)
Halberd
Norfair
Pokemon Stadium 1
Castle Siege
Mario Circuit
Neutral
Yoshi's Island (Brawl) [Best Starter Stage for Pokemon Trainer, IMO]
Lylat Cruise
Smashville
Final Destination
Brinstar
Delfino Plaza
Pokemon Stadium 2
Onett
Green Hill Zone
Luigi's Mansion
Bad
Frigate Orpheon
Skyworld
Rainbow Cruise
Pirate Ship
Jungle Japes
Unsure
Distant Planet (I keep going back and forth between this one)
Corneria (Rarely play here, for some reason)
Port Town Aero Dive
Green Greens
My comment on the good stages:
Pictochat: Great, I tried to ban this stage and it turns out to be of great help. (whacks head against wall)
Yoshi's Island (Melee): too bad this is banned (I think)
Haliberd: When I was talking about this stage in the legality discussion, I thought this wasn't going to be a starter on any account. I like the music. Good thing it's a borderline starter.
Norfair: WHAT THE ****! I tried to ban this stage (failed), and it HELPS US! IS GOD TRYING TO TOY WITH ME HERE?!
PS1: WHOH-HOH! When I started talking about PS1, I was going for Starter. I gave up after the immense opposition, but the Back Room voted partially in my favor (Borderline starter). MY FAVORITE STAGE IS PT'S FAVORITE TOO!
Castle siege: this is because it's the same principal as PS1 isn't it? It has the same legal ranking too.
Mario circuit: This is borderline ban, don't count on it much.
On mid stages:
Yoshi's Island Brawl: technically, it's the best pure starter for PT, not the best.
Lylat: Hmm, interesting, and I thought this was going to be neutral until the BRoom voted on these things
Smashville: Well duh
Final Destination: WELL DUH!
Brinstar: can someone explain this?
Delfino Plaza: this too, considering similarities to Castle Siege
PS2: No comment
Onett: See Mario Circuit
Green hill zone: no comment
Luigi's mansion: the pillars are a factor aren't they?
Stages Bad for PT:
Frigate Orpheon: ******! and I like the music too.
Skyworld: you don't have to worry much here, it is borderline ban too.
Rainbow Cruise: FINALLY! somebody hates this stage as much as I do.
Pirate Ship: ?
Jungle Japes: ???
They have no Idea:
Distant planet: I have no Idea either
Corneria: I just don't like it
Port Town: Look, most of the stage can kill you if you are standing still, I hate this stage a lot
Green greens: no idea either