These metaphoric usages are similar, but not identical. Stuck in a rut refers to a wagon wheel getting stuck in the rut (deep channel) created by earlier wagons passing over soft ground. It's more about being bogged down / unable to move, rather than forced to remain on a fixed path.
Stuck in a groove refers to the needle (stylus) of a record-player. Those of us old enough to remember that technology will recall vinyl discs with scratches / cigarette burns. At a standard 33rpm turntable speed, you'd get the same 2 seconds repeated as the needle reached the damaged part of the inward spiral, and was bumped outwards on each revolution. Reflecting that, the metaphoric usage of OP's example always implies repetition.
My Chambers defines in a rut as following a tedious routine from which it is difficult to escape. Note that this is widely understood even without the word "stuck", or any special context. Few dictionaries would define stuck in a groove; the imagery is transparent, and it's not very common.
So the economy is stuck in a rut doesn't imply anything repeating - just that economic indicators remain at low levels (down in the rut); they can't "break free" and rise to a higher level.
If you say someone's in a groove with no other context, you might mean he's daydreaming, wholeheartedly enjoying something, or in the zone, rather than trapped in tedious repetition. You really need the word "stuck" to clarify the meaning.
In short, rut has greater applicability, in that it's not restricted to "cyclical" or "boring" contexts.
Here's an NGram showing that [stuck] in a rut is the more common form. Many of the relatively small number of instances of stuck in a groove are either unrelated literal usages, or they explicitly explain the metaphor. It's already a fading metaphor anyway, since we don't use records and needles any more.
Best Answer
1) Whichever is less
Among very few things (two preferably)
2) Whichever is lesser
Used for comparing among two or more number of things
3) Whichever is the least
The thing which is less than all of the other things
Yes, they all may sound like they have the same meaning, and it's mostly up to you whatever sense you want to deliver to the reader.