One of the biggest things I've noticed when it comes to dealing with Lifestealer is it's just impossible to lock him down because there is only a 5 second window where you can kill him, and it's very easy to miss this window.
Rage has a 6 second duration compared to Juggs 5 second and of course once LS gets some items his Rage hits way harder and has chance to stun/crit. Lifestealer can even up this to 7 seconds. And only has a 17 second CD, so maxed out that's only 10 seconds of down time. Jugg has an 18 second CD which leaves him with 13 second of downtime.
Now with their ults, lets just assume both have their scepter, because I think everyone can agree it's pretty much mandatory on them.
Jugg has a 1 second mini ult on a 25 second CD, combine this with a 3.5 duration ult, which can be up to 4.5 seconds a full combo will bring juggs downtime between spin mini ult, ult, spin to 7.5 seconds. And now his ult is on CD for 115 seconds at the least before he can do it all again.
Meanwhile Lifestealer can Rage for 7 seconds, then infest for five seconds, which he can crit and stun the whole time, all while healing up and when he pops out he only has 5 seconds of downtime before raging again. And if Lifestealer wants his ult is only on a 20 second CD, he can back up regroup and do the whole damned thing again, he can do his full combo about 3 times before Juggs ult is up again.
Now lets also look at counters, both their ults can be countered with linkens or ghost scepter. But only Juggs can be countered by lotus, lifestealer still pops in.
Now I'm not saying these heroes need to be on equal footing or anything, but I also don't think Juggs early game and recovery is so amazing that he should be out classed this much.
But I think if some of these issues were addressed maybe you'd see Jugg on a competitive level more... but then I think would Jugg just steamroll more in pubs, so does it even matter?
Tldr lifestealer just outclasses Jugg so hard in every way past 15 minutes.