Yes thats fair. There is pre Liverpool Benitez and post Liverpool Benitez.
He got very lucky to win the CL with Liverpool but probably quite unlucky not to win the league. That being said, towards the end he started spending huge sums of money on ordinary players, and picked a fight with the owners to distort the narratives which the KKKult took hook line and sinker.
After that, all I have seen is a manager who has gone to European Champions Inter and left them mid table. Went to European Champions Madrid and left them getting annihilated by Barca. Went to Chelsea and became the first manager post Roman to finish outside the top 4. Went to Newcastle and took them from being out of the relegation zone to being relegated. It's pretty ordinary.
Most Kopites go on about him as if he's in the same league as Mourinho, Guardiola et al. He's not for me. He's a similar level to Koeman, Pochetino, Emery etc, guys a level below the elite managers.
That being said he is very strong tactically and get win set piece games very well. I think he'd be completely the wrong choice for where we look to be going re Walsh, Moshiri and youth investment. If a certain Russian came on board and started lashing money about though I could see him being a potential Mancinish type of fit and work quite well for us. The ex Liverpool thing really doesn't bother me, in fact it's a major attraction. If he won a trophy with us before Klopp won anything with Liverpool it would lead to massive splits in the reds which would be absolute hilarity.