Tiger is generally a better build for solo queue in all elos because early advantages matter a lot and you don't want to rely on your team to carry. However, tiger is single target so you will clear jungle camps and push lanes slower. Unlike Phoenix, you want to be pressuring enemy champs very early with tiger (Level 3 onwards).
Phoenix is better for tanky builds because the base damage is better late game and it's aoe. Phoenix is good for split pushing and powerfarming and will generally you want to peel for your teammates instead of running straight at enemy carries. Phoenix will get you more gold from taxing lanes and clearing jungle camps but you will lose some early pressure because the first few ranks in Phoenix don't do enough damage to pressure enemies hard.
If you look at the high elo Udyr players in NA and Korea, you'll see that most NA Udyrs play offensive styles (Rank 1 plays tiger+phoenix and Rank 2 plays Tiger/Turtle with warrior) but if you look at Korean Udyrs almost all of them play supportive styles (Most run Phoenix/turtle with juggernaut/iceborne. Some don't even get the iceborne). Both are good but for lower elos, tiger has much more pressure early on and gives you extremely strong dueling ability. In higher elos it doesn't really matter which one you use, you can choose according to your team (if you have all squishy carries you can go phoenix and peel for them).
For me there's no real deciding factor, I think all builds have their merits but I play the one that I feel like I have the most success on currently (I played full tank Phoenix/Turtle to diamond last season, then wriggles+trinity phoenix/turtle to diamond 3 100lp. This season I started with full tank Phoenix/turtle but also used warrior+trinity Tiger/Phoenix. Right now I prefer the Tiger/turtle build with warrior). I think that the two most effective builds are tiger turtle and phoenix turtle because turtle stance makes you extremely tanky in fights and will get you out of a lot of situations alive. Tiger/Phoenix has a lot of damage but I don't like not having turtle stance.
The other two junglers that I main are Sejuani and Hecarim, but they have different styles than Udyr. The closest thing I could think of would maybe be Skarner or Volibear.
In any elo below high plat I wouldn't worry about finding a backup champ. You can blind pick Udyr into basically anything in silver and still do well. Tiger/Turtle will work amazingly in lower elos, as will Phoenix/Turtle with an offensive build.