I have not used lantus, but I do use levemir. Both are medium acting basal insulins. Levemir works best injected twice a day. I inject just before going to bed (22 units), and when I wake up in the morning (8 units). As you can see, I don't use the same dose morning and evening, as I find I need more basal insulin at night when I am inactive, than during the day when I am active.
You will need to adjust your dosage based on your target blood sugar levels.
Another new basal insulin is tresiba. This is a long acting basal insulin and is only injected once a day. Many people find it gives more stable blood sugars than some of the other basal insulins. You may wish to ask your Dr about this insulin.
My insurance company pushed me to make that exact switch a few years ago, and I'm pretty happy with it.
Biggest difference is that Levimir release cycles last around half as long as Lantus, which makes for 2 basal shots a day, and it's a little easier to accidentally overlap doses. For example, I try to get my shots at 7am and 10pm, but that creates a 3-hour overlap and gap on either end.
Getting the dosage right makes it easy to work around, but it's only as good as the consistency in your schedule. With Lantus, I focused on getting to sleep around the same time every night, but now I have to also focus on waking up early on the weekends too.
The other thing I liked about the switch was being able to use a flex pen instead of a vial. Not sure if Lantus comes in pens now, but that was a big benefit when I switched. No more syringes, just flexpen needles for everything.
Insurance forced me transition from Lantus to Levemir in February, and I haven't seen any difference in effectiveness. I am only taking one injection before bed, and it's worked just as well as Lantus in keeping my morning numbers in range. The biggest difference I noticed was that Lantus would burn every time I injected and Levemir does not.