The term EO Step refers to the 3x3x3 first substeps which orient all the edges while simultaneously solving other pieces. They are most commonly used in the ZZ method, although they can be applied to other methods as well.
The steps are ordered from easiest to hardest.
EO+X consists of firstly orienting all twelve edges and then solving other pieces separately. For example, EO+Line would be to solve EO and then the DF and DB edges, while the latter step is not influenced in any way during EO. Although very easy and often used by beginners, this approach makes the solve less efficient and require at least two looks.
- Allows for more efficient ZZ F2L by being able to use F2 and M' U2 M.
- Very easy to plan which leads to easier inspection.
- DF edge needs to be solved later.
- F2 and M' U2 M in the middle of the solve often require regrips and might not save as much time.
- Lookahead can be hindered by the unsolved DF edge.
- ZZ F2L is fully <RUL(D)>-gen.
- Because of blockbuilding, solves can be very efficient.
- Lots of regrips are needed during blockbuilding.
- L/R switching requires regrips as well.
- Blindspots can cause pauses to search for pieces.
EOEdge (or Line On Left) is an EO step initially invented for SSC, although it can be used in ZZ via ZZ-LOL. It is similar to EOLine, except that the line is made of the FL and BL edges rather than DF and DB.
- ZZ F2L can be solved <RUD>-gen which is undisputably better than using R, U and L moves.
- While regrips still exist, they aren't as bad as in EOLine.
- Solving with EOEdge is as efficient as with EOLine.
- Similarly to Cross on left, lookahead is enormously hindered, so searching for pieces and the resulting pauses are very common.
EOArrow was proposed by Brayden Mossey and Alex Maass for the Hawaiian Kociemba method, but can also be applied to ZZ where it is the second most used EO Step for two-handed solving (after EOCross). In the variant for ZZ, one solves the arrow edges (usually DF, DL and DB or DF, DR and DB for left-handed people), followed by two F2L pairs on L (or R) and the right (or left) block. In Hawaiian Kociemba, the only difference is that the DR edge remains unsolved.
- Movecount is lower than in EOCross.
- Less regrips than EOLine.
- Most regrips are executed with the solver's dominant hand.
- The solver needs to do less L/R switching than in e.g. EOLine and EOArrow.
- Less blindspots than EOLine, especially when right block is being solved.
- Right block can be solved fully <RU>-gen.
- Due to the above, higher TPS can be reached than with EOLine.
- Higher movecount than EOLine because of specified order.
- More regrips than EOCross.
- Harder to inspect than EOLine.
EOCross was invented when CFOP users applied the Cross to ZZ. So instead of only two D layer edges, all four are solved. The rest of the F2L is solved using CFOP-style F2L pairs. Nowadays, it is the most common way to do ZZ two-handed.
- The Cross allows for almost regripless ZZ F2L.
- Due to more pre-solved pieces, less blindspots exist.
- Because of this, very high TPS can be reached.
- Inspection becomes a lot harder and is comparable to that of an XCross.
- Due to solving all D layer edges, ZZ F2L becomes 7 moves less efficient when compared with EOLine. 
Since WaterZZ has a completely different approach to ZZ, it can't be compared with the other steps.
XEOLine (or also called XEOArrow) is when an EOLine and a 2x2x1 block (usually on L) are solved simultaneously. This is inspired by XCross and is a very advanced version of EOLine and EOArrow. The normal approach to continue the solve is to solve the remaining F2L pair on L and then a block on R.
- If planned well, the movecount is significantly better than that of EOLine.
- After the pair on L, no L/R switching is required.
- The solve is finished <RU>-gen.
- Regrips are reduced because of the already solved 2x2x1 block.
- Most regrips are performed with the solver's dominant hand.
- XEOLine is a lot harder to plan than normal EOLine and needs lots of time to master.
- Like in EOArrow, some regrips still exist.
- Very ergonomic (especially for One-Handed Solving because ZZ F2L can be finished using only R, U, r2 and M2 moves.
- No L/R switching because of the movegroup.
- Planning is slightly easier because centers can be an M2 off.
- Very hard to plan all of it in inspection.
- Regrips during the rest of the solve.
XEOCross is an extension of EOCross and XEOLine which solves all D layer edges and a 2x2x1 block in DBL (as opposed to only the D layer edges in EOCross and only line edges + 2x2x1 block in XEOLine). It could be compared to XXCross in difficulty.
- The Cross allows for almost regripless ZZ F2L.
- Due to lots of pre-solved pieces, almost no blindspots exist.
- Since EO, Cross and first pair are solved simultaneously, this has a lower movecount than EOCross.
- As only on pair on the left remains, less L/R switching exists (and could be completely removed by solving <RrUF(D)>-gen).
- Because of the very good ergonomics, very high TPS can be reached.
- Inspection becomes a lot harder and is comparable to that of an XXCross (2x2x3 block + edge).
- While more efficient than EOCross, XEOCross is still less efficient than EOLine.
EO223 in one step (what Petrus achieves in three and LEOR in two) would be the ultimate EO Step. However, it seems pretty much impossible to plan it every time, although if it can be planned, the results usually are really good solves like Yusheng Du's 3.47 WR single.