The 5/8 wave mobile antenna will work best if you are in flat, open country and need the most range to reach repeaters or other stations on simplex which are at or slightly over your radio horizon.
A 1/4 wave antenna has a "fatter" radiation pattern and a high radiation angle which is much better for getting up, out and around terrain and obstructions. If you have to operate mobile while driving down a valley surrounded by high terrain in Colorado or even West Virginia or Pennsylvania, where most repeaters are up high on a mountain somewhere, a high gain antenna with a flat, narrow radiation pattern down on the horizon is NOT what you want. Ditto if you are down or out on the water and the repeater is on a high broadcast tower ashore miles away. With a 5/8 wave you may be stuck in an RF "hole."
A quarter wave antenna when used with a ground plane is unity gain and low profile which works well in most indoor garage situations. Its wider pattern and higher radiation angle give you better multipath probabilities which may make a difference between "getting out" or not.
For instance, my hunting cabin in Berkeley County, WV in FM09 is at 600 ft. AMSL and on on a "bench" a mile behind and below the crest of North Mountain, which is 1083 ft. elevation near my location. My home repeater is a single-site machine in Tyson's Corner, VA, FM18, about 70 air miles away. When using a high-gain stick or even a beam I cannot stay reliably in the repeater, because the radiation pattern can't get over the terrain, but a simple unity gain antenna on the cabin roof does!
A half-wave antenna does not require a ground plane and is provide the same unity gain on a fiberglass truck cap, or auto window glass mount that a quarter wave does with a ground plane. You can use a ground plane with a 1/2 wave and get about 2 dB gain.
For most single-band 2-meter users I think a 1/2 wave is the best choice for all-around use. Many "dual-band" mobile antennas are 1/2 wave on 2 meters and two 5/8 stacked colinear elements on UHF, which is also a great compromise.
Your mileage may vary, but those are my two cents.