Among proper all-rounders, the greatest one has to be Sir Richard Hadlee.
There are several players who batted & bowled with different hands (Batting is 2 hands job, but normally we consider bottom hand as the main hand), but hardly any of them were significantly good in both.
Among such ambidextrous players, after Sir RJH, randomly I can recall RJ Shastri, C Gayle, Clive Lloyd (he was quite decent right arm medium pacer), Wasim Raja (He was Right Arm leggi), Faulkner, Greg Methews, Johnson (ZIM), A Giles, Wilfred Rhodes, Frank Worrell, BC Broad, Moeen Ali, Ben Stokes, Lance Kluesner comes to mind.
Finally, there are several cricketers, who were significantly strong in one suit while hardly any contribution with others. I can recall BC Lara, Ul Haq, Sanga, Gower, Ganguly, Ambrose, Anderson, Boult, Josh Hazzlewood, Bishen Singh Bedi, Dudley Underwood, Stefan Fleming, Damien Fleming, A Cook, Shiva, G Smith, MJ Clarke, M Hayden, Langer, Kirsten, Mike Hussey, Warner, Treskothick, DC Compton, Gilchrist, Andy Flower, Gambhir, Tamim, Larry Gomes, Arjuna, Ijaz, Butt, Fahim, Talat, Mominul ... comes to mind, and I am missing MANY.
One technical note is, over 90% people are born with natural right-hand. But, cricket is a top hand game, therefore there are several batsmen who actually used their strong hand as the top hand (like Lara, Gower, Sanga, Ul Haq); but one has to bowl with stronger hand. For that, we see lot, lot more left-handed batsman than left-arm bowlers, though in recent times in PAK we see a different trend.
In this category, we'll see most number is strong lefti batsmen but poor right arm bowler; followed by strong left arm blower, but weak right-hand batsman. Ul Haq & Ijaz are very rare who being left-handed opted to bat right hand and Ijaz was probably the only player who used lefy arm to bowl, but batted right handed and he was predominantly a bottom hand (right hand) batsman, whose right arm was naturally week.
Also, I believe Tendulkar writes and plays tennis with left hand, but his cricket is full with right hand - even never recall him throwing with left hand; while Lara & Sobers (?) were left handed & right handed golfer respectively, but bowled with other arm. Someone should check - Wasim plays golf right handed, but not sure.
This PAK kid some Jan is unique of all - can bowl legal balls with both arm; but I think he needs to do a bit better to come in this list - that's play for PAK at least for one International.