This is just off the top of my head, as it were. Feel free to add comments and I will update.
1. Portable (unless it's a very large item)
2. Easy to hold against body and figure out required no. of stitches
3. You can knit any stitch you like, and change at any point. The sky's the limit
4. Knitting in the round or in a circle (eg the bottom of a shopping bag) is fairly easy with some planning
5. Increasing or decreasing within a row of stitches is simple
6. Fixing mistakes is usually very easy unless it's a complex lace pattern
7. Garter stitch is a breeze
1. Can be slow and tedious, especially on larger or plainer garments
2. Knitting needles can escape in transit
3. Complex lace patterns can be very slow-going and lifelines and patience will be required
4. Circular knitting requires either interchangeable needles (differing cable lengths) or a large collection of lengths - or the dreaded DPNs (double-pointed needles)
Machine knitting (Japanese machines)
1. Very fast
2. Lovely neat stitches, lovely even tension
3. Makes lace knitting a breeze (even if it requires a second carriage to accomplish it)
4. Will do patterning such as two-colour fairisle, two colour slip etc, with ease once programmed
5. Circular knitting from 5 stitches to 400 possible if ribber attached (total sts available dependant on machine)
6. With machine knitting you will finish a project as opposed to handknitting,when you may get sick of it
7. Complex techniques such as double-faced knitting = DBJ on a machine - pretty nippy if you have a ribber and can program it in.
8. Some techniques eg tuck, plating, knitweave, rarely used in hand-knitting, are a breeze on the machine.
1. Bit of a steep learning curve at first, and not many colleges run classes anymore
2. Cannot knit and purl in the same row unless (a) you have a ribbing attachment or (b) you are using a garter carriage (Brother/KnitKing standard gauge machines only) - in other words, garter stitch is so tedious in most cases as to be not worthwhile unless it's for small amounts, also other knit/purl combos eg moss stitch, block stitch.
3. Not portable, and rather noisy. You will be banished to another room! :)
4. Increasing or decreasing within a row of stitches is difficult without a garter bar. You can also use waste yarn and rehang the work, which is a bit tedious. I try and redesign patterns to avoid it eg knit from the opposite direction.
5. Fixing mistakes can be tricky - sometimes it's quicker to start again.
6. Weights are important, especially for ribbing, so mind your toes.
7. You will need different machines for different yarn thicknesses - no one machine can cope with both 2ply and chunky yarn. Technically, the convertible KX machines can do both, but the 2ply will come out like netting, and the chunky might come out like cardboard.
8. Slipped stitches - yarn is always slipped on the purl side. If you want it on the knit side that will require hand-manipulation
9. Mixing purl with other stitches cannot be done without lots of hand-manipulation (see also 2) - eg gutters for cables will have to be reformed by hand with the latch tool unless you can bring your ribber into play.
Machine knitting (Passap)
1. Very fast (even faster with a motor)
2. Steep learning curve - the E6000 manual assumes you already know how it works
3. Lovely neat stitches, lovely even tension
4. Pusher system means each needle can be manipulated for patterning on the fly - front bed can be fully automated by punchcard or electronics, back bed is semi-automatic ie pusher position can be alternated on every row or every other row
5. Can produce amazing textures with tuck and slip, as machine uses pushers to hold knitting in place
6. E6000 passap is pre-programmed with lots of stitches, with almost limitless combinations available.
1. Even more steep learning curve. Being a true double-bed, it can be hard to see the work as it progresses as the front bed does not drop down very far (Japanese ribbers are optional and can be added later)
2. Machine can only carry one colour at a time, so fairisle is time consuming.
3. Fixing mistakes can be very tricky - visibility being the main problem (the front bed only drops down about an inch).
4. Cannot do knit and purl in the same row unless it's ribbing, or you are using a transfer carriage as part of the pattern (which can be quite slow)
5. No plating (unless you are lucky enough to own a Mercer plating device).
6. Some kinds of lace can involve a transfer carriage (which is an optional extra). Otherwise, it's hand manipulation only.
7. You will occasionally need weights, despite what the literature might say
8. Only standard gauge machines available, so not suitable for chunky yarns