Theres no comparison between Ancelotti and Klopp as far as I'm concerned (Ironic cause I've done as detailed a comparison as I could below). Just look at the CV, record, and transfers of both. The safe option is definitely Ancelotti; he'd also be the statement of intent FSG need to put out after a string of bad calls.
CV:Carlo: Parma, Juve, Milan, Chelsea PSG, R.Madrid (experience in England; continental experience)
Klopp: Mainz, Dortmund
Record: Ancelotti: 3 champions leagues, 3 eufa cups, 2 fifa club world cup, and league titles in England, France, Italy, and Spain + many domestic cups.
Klopp: 2 league titles.
Note: Ancelotti doesnt have bad seasons does he; You could make a case for him having a better record than any manager in world football today! Got a standing ovation from Madrid fans and the media when he was sacked. Says something about how highly they thought of him at the best club in the world a few months ago. Klopp is almost universally loved by fans and media for the character he is.
Transfers:Ancelotti: Bought more world class players than any manager in world football. And he's done it consistently over 20 years. Hardly signs a flop:
1996 (Manager of Parma. His second season as a manager anywhere ; 1st in the top flight)
Signs: Thuram, Crespo, Chiesa [total spent: 4.45mill]
All 3 of them combined cost less than 3.5mill pounds. 2 of the best forwards in the recent history of Serie A and one of the best defenders in football history. Went on to finish 2nd in the league only losing the title to Juve by 2 points after Juve snatched a draw from a controversial penalty.
1997 (Second Season at Parma)
Signs: Blomqvist, Fiore [total spent: 4.48mill]
1998 (joins struggling Juve in Feb, gets them to CL semis)
1999 (first full season at Juve)
Signs: Van Der Sar, Kovacevic, Zambrotta, Tudor, Maresca [total spent: 27mill]
Loses title on final day by a point after defeat.
2000
Signs: Trezeguet (16mill)
Jan 2001-2009 Milan
Signs: Nesta (21mill) , Seedorf (15mill), Rivaldo (free) , Kaka (5.7mill), Cafe (free), Stam (7mill) , Ronaldo (5mill) , Pato (15mill) , Ronaldinho (17mill) , Thiago Silva (7mill) , Gilardino (17.5mill*)
2009-2011 Chelsea
Signs: Sturridge (5mill), Matic (1.2mill) , Torres (50mill*), David Luiz (17.5mill), Ramirez (15mill)
Jan 2011-2013 PSG
Signs: Thiaggo Motta (8mill) , Maxwell (2mill) , Thiago Silva (29mill) , Lucas Moura (28mill) , Lavezzi (20mill) , Zlatan (14mill) , Veratti (8mill) , Beckham (free)
2013 -2015
Signs: Bale (80mill) , Illaramendi (22mill) , Isco (21mill) , Carvajal (4mill) , James Rod (56mill) , Toni Kroos (21mill) , Keylor Navas (7mill)
I have included all players signed for over 15mill (Zhirkov at 14.5 is also an Abramovic flop), Gilardino and Torres are the only 2 big money flops I found. Gilardino scored 17 and 12 LEAGUE goals in his first 2 seasons at Milan, spent his 3rd season mostly at the bench scoring 7 before leaving at the end of the season; he contributed to them reaching the CL final in 2007 which they won against us.
Klopp: 2008: Subotic
2009: Hummels, Bender
2010: Lewandowski, Kagawa
2011: Gundogan
2012: Reus
2013: Mkhitaryan, Aubameyang
2014: Immobile (flopped)
Note: Klopp knows the German market and has had success buying lower reputation players domestically at low cost. Ancelotti's experience across different leagues and his reputation would be a big draw in the transfer market.
Tactics:Ancelotti: Changes formation based on the side he manages. Played a 4-4-2 diamond in most games with title winning Chelsea when they had Anelka-Drogba leading the line. 4-3-3 with Madrid.
Klopp: Has almost exclusively played 4-2-3-1 with Dortmund over the past 5 years.