Here's my writeup.
Gunla
feel free to edit and tinker with as needed. Its a work in progress and I'll either be finishing it tonight or tomorrow.
Lucina's placement compared to Marth is an issue that is brought up quite often, and it is again the case with the new tier list. Why is Lucina, a character that is almost identical to Marth, not right next to him/tied with him on the tier list? Before we dive into this with more detail, let's start off by pointing out in earlier patches, Marth and Lucina were indeed much closer to eachother. But overtime, the list of buffs they received helped Marth more in the longrun than Lucina. This is in addition to the inherent advantages the tipper mechanic has in many situations. Let's break it down:
Let me preface by briefly covering how their swords work.
Lucina does not have a tipper, but her sword does what is approximately inbetween a marth tipper and non tipper in terms of damage and knockback along the entire blade (I can hunt the exact stats later; pretty sure they are in the Marcina boards). This brings up the fact that Lucina gets more damage out any attack that is not tippered compared to Marth. For a good while, this was the cornerstone of the pro Lucina argument: Unless you were perfect, Lucina could potentially be more beneficial in the longrun since you will not be landing every single attack as a tipper, no matter how good you are as a player.
With that aside, lets dive in.
First, the patch changes that affected Marth and Lucina. There were multiple patch changes that affected them roughly the same (IE slight % increases in damage here and there), but there were two patch changes in particular that helped Marth especially.
The big one: The shield stun changes.
When the patch rolled around that introduced increased shield stun (I need to go back and double check which one), this had a massive impact on Marth. Tippers induce a lot more shield stun on an opponent. The result of this is that Marth can be much safer than Lucina when attacking a shielding opponent. With proper spacing, his tippers moves can be much harder for a shielding opponent to punish. Having this huge safety advantage over Lucina pays massive dividends, especially when having to face down top tier characters where a couple frames can mean the difference between being safe and being punished.
The 2nd change is the downthrow change. This change allows Marth and Lucina to use down throw as a more effect combo starter and 50-50 creator. The difference is Marth gained true tipper combos from this, giving him another guaranteed way to deal out maximized damage. This is something Lucina doesn't gain since she has the same hitbox all around.
All of Marth and Lucina's A moves follow the same principle for the most part: Marth's will be better if spaced, Lucina's will be superior if not. Marth can gain some better combos though by hitting with untippered moves, which will lead into tippered follow ups easier.
Their grabs and throws are exactly identical. Both do the same things at the same %s
Their Special moves is where it has been argued Lucina has an advantage. But does she really? Depends.
(B) Shield breaker: Although Lucina's is still a powerful move, Marth's give the strongest chance to break shield while charging the least amount of time due to tippers. Both have stock ending potential though.
(Side B) Dancing blade: In general, Lucina's is much more reliable in terms of KO potential. The last hit of Lucina's side b is pretty strong and can end stocks at decent percents. That being said, Marth's can tipper more often than people realize. Following an opponents DI and ending it with a side direction or up direction attack pending their DI can net you a tipper quite often, as well as just bad DI from an opponent. As you can imagine, this can net super early kills.
(up B) Dolphin slash This move is pretty much better for lucina in most situations. Most times this move is used to recover, a combo finisher, or as an out of shield option where it is very hard to control spacing. Lucinas will result in more consistent KOs.
(down b) counter: Again, a toss up. Marth's will have the edge here though I believe, as in a lot of situations you should be able to not only read an opponent's move to counter, but properly space yourself to hit with a tipper. Sometimes though, spacing is impossible.
Lucina also has a fatal flaw in her design. In most matchups, despite having the ability to do consistent damage anywhere on the blade, she has to play the spacing game anyway to be the safest. So essentially, so has to play like marth and go for tippers to remain as safe as possible anyway. In these situations, you are being directly gimped by not being Marth in a matchup where you have to play like Marth. A straight downgrade.
Last but not least, results. This section speaks for itself. Marth has much better and consistent results in the current meta. Players my Mr.E and Pugwest have put up solid results with Marth, top 16ing major events. Meanwhile, Lucina is nowhere to be seen in those higher placings.