Is a Muslim who does not follow the teachings of Islam worse than an atheist?

The Muslim is obliged to adhere to the teachings of his
religion and perform the obligatory duties of praying, fasting, honouring
his parents, upholding the ties of kinship, speaking truthfully and other
duties that Allaah has enjoined upon him. 

He must also avoid that which has been forbidden, such as
zina (unlawful sexual relations), riba (usury or interest), drinking
alcohol, disobeying parents, lying, treachery, consuming people’s wealth
unlawfully and other forbidden things. 

This is obligatory upon every Muslim. Whoever adheres to that
will be close to Allaah and beloved to Him, and is promised admittance to
Paradise and being honoured by Him. 

Those who neglect the obligatory duties or commit forbidden
actions fall into two categories: 

1 – Those whose sin reaches the level of kufr (disbelief) and
shirk (associating others with Allaah), such as mocking the faith, insulting
Allaah, insulting His Messenger, denying any of the well known tenets of
Islam, or regarding as permissible something that Allaah has forbidden, such
as regarding wine, adultery or pork as permissible. Whoever does that is an
apostate from Islam, but if he does that out of ignorance or negligence,
then he should be taught, advised and reminded, so that he may repent to
Allaah. If he persists in that after being taught, then he is an apostate
who is beyond the pale of Islam. 

2 – Those who commit some sins that are not regarded as kufr
or shirk, such as adultery or drinking wine, without regarding that as being
permissible. If such a person repents, Allaah will accept his repentance and
turn his bad deeds into good deeds. But if he persists in his sin, then
Allaah warns him of the painful punishment on the Day of Resurrection, and
of punishments in this world, such as poverty, sickness, humiliation and
defeat, as well as having the hadd punishment carried out on him when
committing some crimes, such as drinking alcohol or committing adultery, if
it is proven that he committed the crime, and subject to certain conditions
that we do not have room to discuss here. 

The Muslims’ duty towards those who commit sin is to advise
them and call them to repent, and remind them of the danger of sin and the
evil consequences thereof, as well as hating them because of their sin. 

The obedient and the disobedient are not equal before Allaah,
or before His believing slaves, as Allaah says (interpretation of the
meaning): 

“Shall We treat those who believe (in the Oneness of
Allaah –– Islamic
Monotheism) and do righteous good deeds as Mufsidoon (those who associate
partners in worship with Allaah and commit crimes) on earth? Or shall We
treat the Muttaqoon (the pious) as the Fujjaar (criminals, disbelievers, the
wicked)?”

[Saad 38:28]

But if a sinner does both
good and evil, and does both acts of obedience and acts of disobedience –
and chief among goodness is belief in Allaah – then the justice and mercy of
sharee’ah dictates that his good deeds should not ignored or wasted, and he
is not to be regarded the same as those who disbelieve in Allaah
altogether. 

With regard to a Muslim marrying a kaafir woman, this is
haraam, unless she is a Jewish or Christian woman, for Allaah has allowed
marriage to them, because of the possibility of their being guided to Islam
and because these religions share with Islam the belief in Allaah, the
Prophets and Messengers, and the Last Day. The marriage of such a woman to a
Muslim may lead her to seek the truth and encourage her to give up her
disbelief in Muhammad (peace and blessings of Allaah be upon him) and
his message. 

To sum up: 

The Muslim who leaves his religion altogether is as bad as an
atheist, or worse. 

As for the Muslim who believes in the basics of Tawheed
(Oneness of God) and Islam, but he commits major sins and abhorrent actions,
he is undoubtedly better than a kaafir and atheist – despite his
shortcomings – because the good deed of Tawheed (believing in the Oneness of
Allaah) is the best of all good deeds, and he has done that. But he is
warned of a painful punishment in this world and the Hereafter for the sins
he commits, if Allaah does not bestow His mercy upon him and forgive him. 

And Allaah knows best.